# FIND COORDINATES OF CENTROID OF TRIANGLE

## About "Find Coordinates of Centroid of Triangle"

Find Coordinates of Centroid of Triangle :

Here we are going to see some example problems on finding centroid of triangle.

The centroid G of the triangle with vertices A(x1, y1), B(x2, y2) and C(x3, y3) is

G [ (x1 + x2 + x3)/3, (y1 + y2 + y3)/3 ]

## Find Coordinates of Centroid of Triangle - Practice questions

Question 1 :

Find the centroid of the triangle whose vertices are

(i)  (2, −4), (−3, −7) and (7, 2)

Solution :

Let the points be A (2, −4) B (−3, −7) and C (7, 2)

=  G [ (x1 + x2 + x3)/3, (y1 + y2 + y3)/3 ]

=  (2 - 3 + 7)/3, (-4 - 7 + 2)/3

=  (6/3, -9/3)

=  (2, -3)

(ii)  (−5,−5),  (1,−4) and (−4,−2)

Solution :

Let the points be A (−5,−5) B (1,−4) and C (-4, -2)

=  G [ (x1 + x2 + x3)/3, (y1 + y2 + y3)/3 ]

=  (-5 + 1 - 4)/3, (-5 - 4 - 2)/3

=  (-9 + 1)/3, (-11/3)

=  (-8/3, -11/3)

Question 2 :

If the centroid of a triangle is at (4,−2) and two of its vertices are (3,−2) and (5,2) then find the third vertex of the triangle

Solution :

Let the given vertices be A(3, -2) and B (5, 2)

Centroid of the triangle  =  (4, -2)

Let the third vertex be C (a, b)

=  G [ (x1 + x2 + x3)/3, (y1 + y2 + y3)/3 ]

(3 + 5 + a)/3, (-2 + 2 + b)/3  =  (4, -2)

(8 + a)/3, (b/3)  =  (4, -2)

By equating x and y-coordinates, we get

 (8 + a)/3  =  48 + a  =  12a  =  12 - 8a  =  4 b/3  =  -2b  =  -6

Hence the required vertex is (4, -6).

Question 3 :

Find the length of median through A of a triangle whose vertices are A(−1, 3), B(1, −1) and C(5, 1).

Solution :

If we draw a median through A, it will intersect the side BC exactly at middle.

Mid point of the side BC  =  D

=  (x1 + x2)/2, (y1 + y2)/2

=  (1 + 5)/2, (-1 + 1)/2

=   (6/2, 0/2)

=  (3, 0)

Length of median AD  =   √(x2 - x1)2(y2 - y1)2

=   √(3 + 1)2 + (0 - 3)2

=   √42 + (-3)2

=   √(16 + 9)

=   √25

=  5 units. After having gone through the stuff given above, we hope that the students would have understood, "Find Coordinates of Centroid of Triangle"

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